Commutator of the matrices of the rotation group

1,340
30
Consider the rotation group ##SO(3)##.

I know that ##R_{x}(\phi) R_{z}(\theta) - R_{z}(\theta) R_{x} (\phi)## is a commutator?

But can this be called a commutator ##R_{z}(\delta \theta) R_{x}(\delta \phi) R_{z}^{-1}(\delta \theta) R_{x}^{-1} (\delta \phi)##?
 

Fredrik

Staff Emeritus
Science Advisor
Gold Member
10,730
405
I haven't seen anyone use that term for anything other than expressions of the form AB-BA.
 
1,340
30
I found it in page 31 of Ryder's 'Quantum Field Theory' - second edition.
 

Related Threads for: Commutator of the matrices of the rotation group

Replies
39
Views
2K
Replies
5
Views
3K
Replies
5
Views
10K
Replies
2
Views
5K
Replies
3
Views
1K
Replies
1
Views
2K
  • Posted
Replies
1
Views
1K
Replies
6
Views
2K

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top